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Three formulas for the Ising and Potts invariants of a knot or link
Abstract
Jones described how the Ising and Potts models from statistical mechanics give rise, with appropriate choices of Boltzmann weights, to invariants of an oriented link. The Boltzmann weights that Jones proposed, however, work only with a correction factor that he does not mention. We fill in the missing details in two different ways. We also show that all of these invariants, which we call the Ising and Potts invariants, are given by evaluating the Jones polynomial at t equal to one of these Boltzmann weights.
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BibTeX
@misc{bullock2026three,
title = {{Three formulas for the Ising and Potts invariants of a knot or link}},
author = {Tristan Bullock and Thomas Kindred},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09093},
eprint = {2609.09093},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09093},
}
RIS
TY - UNPB
TI - Three formulas for the Ising and Potts invariants of a knot or link
AU - Tristan Bullock
AU - Thomas Kindred
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09093
UR - https://arxiv.org/abs/2609.09093
AB - Jones described how the Ising and Potts models from statistical mechanics give rise, with appropriate choices of Boltzmann weights, to invariants of an oriented link. The Boltzmann weights that Jones proposed, however, work only with a correction factor that he does not mention. We fill in the missing details in two different ways. We also show that all of these invariants, which we call the Ising and Potts invariants, are given by evaluating the Jones polynomial at t equal to one of these Boltzmann weights.
ER -